Transformations can be thought of as functions that take the points from one object (the pre-image) to the corresponding points on another object (the image). In the unit, you saw examples of how algebra can be used to rewrite the coordinates of points after they have been transformed. You can also use function notation to rewrite the coordinates. For example, these statements show several different ways you can use function notation for the translation, T, of a point 6 units in the positive x-direction: T(x, y) = (x + 6, y) T:(x, y) = (x + 6, y) T<6, 0>(x, y) = (x + 6, y) T6, 0(x, y) = (x + 6, y) Part A Write functions for each of the following transformations using function notation. Choose a different letter to represent each function. For example, you can use R to represent rotations. Assume that a positive rotation occurs in the counterclockwise direction. translation of a units to the right and b units up reflection across the y-axis reflection across the x-axis rotation of 90 degrees counterclockwise about the origin, point O rotation of 180 degrees counterclockwise about the origin, point O rotation of 270 degrees counterclockwise about the origin, point O Font Sizes Characters used: 0 / 15000 Part B How do these functions differ from functions you have used in algebra in the past? Font Sizes Characters used: 0 / 15000 Part C In the same way that other functions can be combined, a series of transformations can be combined into a single function. For example, this statement for the function S shows one way to represent the rotation of a point 270° counterclockwise about the origin followed by a translation 3 units to the left and 1 unit up: S(270, O)/<-3,1>(x, y) = (y – 3, -x + 1). Write a function to represent each series of transformations: rotation of 90 degrees counterclockwise about the origin, point O, then a reflection across the x-axis reflection across the y-axis, then a translation a units to the right and b units up translation a units to the right and b units up, then a rotatio